Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10 −7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.
Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10 −7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.
Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10−7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the
outside edge of the wheel, as in the figure, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot
in the wheel. One such slotted wheel has a radius of 7.3 cm and 190 slots at its edge. Measurements taken when the mirror is L = 1100
m from the wheel indicate a speed of light of 3.0 x 105 km/s. (a) What is the (constant) angular speed of the wheel? (b) What is the
linear speed of a point on the edge of the wheel?
(a) Number
(b) Number
Mi
Light
Source
Units
Units
Light
beam
Rotating
slotted wheel
Mirror
perpendicular
to light beam
An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel, as in the figure,
travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has a radius of 2.9 cm and 120 slots at its edge.
Measurements taken when the mirror is L = 670 m from the wheel indicate a speed of light of 3.0 x 105 km/s. (a) What is the (constant) angular speed of the wheel? (b) What is
the linear speed of
point on the edge of the wheel?
Light
beam
Light
Mirror
Source
perpendicular
to light beam
Rotating
słotted wheel
(a) Number
Units
(b) Number
Units
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A fiber optic gyroscope is a fascinating device used to measure rotation rate (angular velocity),
which is a necessary parameter to be measured in through autonomous navigation systems (inertial
navigation). They are based on an interferometer conceived in 1913 by the French physicist Georges
Sagnac. In a Sagnac interferometer, a beam of light is split and the two beams are made to follow the same
path but in opposite directions. On return to the point of entry the two light beams are allowed to exit the
fiber loop (see Figure and undergo interference. If the loop rotates clockwise, the clockwise optical path
becomes longer than the counterclockwise optical path (see Figure 2). The phase difference (interference)
is proportional to the rotation rate (angular velocity). Derive this relationship for a fiber optic gyroscope
that uses a 1 km long fiber aranged in a 25 cm spool and a laser beam with wavelength of 1.5 um.
Left-handed light
Optical
fiber coil
Spectroscope
Light source[…
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